What is the answer to (14^{3x+1})(8^{2x+3})=7 ?

The answer to (14^{3x+1})(8^{2x+3})=7 is x=(ln(7)-9ln(2)-3ln(2)log_{8}(14))/(3ln(2)(3log_{8)(14)+2)}

Solve for x: (14^{3x+1})(8^{2x+3})=7

The solution is x=(ln(7)-9ln(2)-3ln(2)log_{8}(14))/(3ln(2)(3log_{8)(14)+2)}

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(1 4^{3 x + 1}) (8^{2 x + 3}) = 7

x = \frac{ln ( 7 ) - 9 ln ( 2 ) - 3 ln ( 2 ) lo g _{8} ( 14 )}{3 ln ( 2 ) ( 3 lo g _{8} ( 14 ) + 2 )}

Decimal Notation

x = - 0.57398 \dots

Solution steps

(1 4^{3 x + 1}) (8^{2 x + 3}) = 7

Apply exponent rules

(lo g_{8} (14) (3 x + 1) + 2 x + 3) ln (8) = ln (7)

Solve

(lo g_{8} (14) (3 x + 1) + 2 x + 3) ln (8) = ln (7) : x = \frac{ln ( 7 ) - 9 ln ( 2 ) - 3 ln ( 2 ) lo g _{8} ( 14 )}{3 ln ( 2 ) ( 3 lo g _{8} ( 14 ) + 2 )}

x = \frac{ln ( 7 ) - 9 ln ( 2 ) - 3 ln ( 2 ) lo g _{8} ( 14 )}{3 ln ( 2 ) ( 3 lo g _{8} ( 14 ) + 2 )}

5^{x} = 22

5^{x} = 23

5^{x} = 14

5^{x} = - 1

3^{2 x + 5} = 3^{7}

What is the answer to (14^{3x+1})(8^{2x+3})=7 ?
The answer to (14^{3x+1})(8^{2x+3})=7 is x=(ln(7)-9ln(2)-3ln(2)log_{8}(14))/(3ln(2)(3log_{8)(14)+2)}
Solve for x: (14^{3x+1})(8^{2x+3})=7
The solution is x=(ln(7)-9ln(2)-3ln(2)log_{8}(14))/(3ln(2)(3log_{8)(14)+2)}